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10. In a small college community of 5000 people, an influenza epidemic starts with 10 cases at t = 0. After 2 weeks, 500 people in the college community have been infected. Treat the spread of this epidemic by a logistic growth model, in which the number of cases (y) satisfies the differential equation M dy = a y( M – y) , the solution of which is y dt %3D where a, M, and C are Mat 1 + Ce constants, andt is the number of weeks since the epidemic began. a) Find the numerical values of the constants "M", "C", and "a". Show all work in detail and write your answers in the spaces provided below. Write a formula for y(t), with the numerical values of the constants plugged in. Your answer should be in the form "y(t) =

10. In a small college community of 5000 people, an influenza epidemic starts with 10 cases at t = 0. After 2 weeks, 500 people in the college community have been infected. Treat the spread of this epidemic by a logistic growth model, in which the number of cases (y) satisfies the differential equation M dy = a y( M – y) , the solution of which is y dt %3D where a, M, and C are Mat 1 + Ce constants, andt is the number of weeks since the epidemic began. a) Find the numerical values of the constants "M", "C", and "a". Show all work in detail and write your answers in the spaces provided below. Write a formula for y(t), with the numerical values of the constants plugged in. Your answer should be in the form "y(t) =

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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10. In a small college community of 5000 people, an influenza epidemic starts with 10 cases at t = 0. After 2 weeks, 500 people in the college community have been infected. Treat the spread of this epidemic by a logistic growth model, in which the number of cases (y) satisfies the differential equation M dy = a y( M – y) , the solution of which is y dt %3D where a, M, and C are Mat 1 + Ce constants, andt is the number of weeks since the epidemic began. a) Find the numerical values of the constants “M", “C", and "a". Show all work in detail and write your answers in the spaces provided below. Write a formula for y(t), with the numerical values of the constants plugged in. Your answer should be in the form “y(t) = M = C = a = y(t)= b) Use your formula to predict the number of influenza cases in the college community 4 weeks after the epidemic began. State your answer in decimal, rounded to 2 decimal places. y(4) =
Transcribed Image Text:10. In a small college community of 5000 people, an influenza epidemic starts with 10 cases at t = 0. After 2 weeks, 500 people in the college community have been infected. Treat the spread of this epidemic by a logistic growth model, in which the number of cases (y) satisfies the differential equation M dy = a y( M – y) , the solution of which is y dt %3D where a, M, and C are Mat 1 + Ce constants, andt is the number of weeks since the epidemic began. a) Find the numerical values of the constants “M", “C", and "a". Show all work in detail and write your answers in the spaces provided below. Write a formula for y(t), with the numerical values of the constants plugged in. Your answer should be in the form “y(t) = M = C = a = y(t)= b) Use your formula to predict the number of influenza cases in the college community 4 weeks after the epidemic began. State your answer in decimal, rounded to 2 decimal places. y(4) =
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